ABSORBING COMULTIPLICATION MODULES OVER A PULLBACK RING
The purpose of this paper is to introduce the concept of 2-absorbing
___
- Y. Al-Shania and P. F. Smith, Comultiplication modules over commutative
rings, J. Commut. Algebra, 3(1) (2011), 1-29.
- D. M. Arnold and R. C. Laubenbacher, Finitely generated modules over pull-
back rings, J. Algebra, 184(1) (1996), 304-332.
- I. Assem, D. Simson and A. Skowronski, Elements of the Representation The-
ory of Associative Algebras, Vol. 1, Techniques of Representation Theory, Lon-
don Math. Soc. Student Texts, 65, Cambridge University Press, Cambridge,
2006.
- [A. Badawi, On 2-absorbing ideals of commutative rings, Bull. Austral. Math.
Soc., 75(3) (2007), 417-429.
- A. Badawi, U. Tekir and E. Yetkin, On 2-absorbing primary ideals in commu-
tative rings, Bull. Korean Math. Soc., 51(4) (2014), 1163-1173.
- A. Badawi, U. Tekir and E. Yetkin, On weakly 2-absorbing primary ideals of
commutative rings, J. Korean Math. Soc., 52(1) (2015), 97-111.
- H. Bass, On the ubiquity of Gorenstein rings, Math. Z., 82 (1963), 8-28.
- M. C. R. Butler and C. M. Ringel, Auslander-Reiten sequences with few middle
terms, with applications to string algebras, Comm. Algebra, 15(1-2) (1987),
145-179.
- Ju. A. Drozd, Matrix problems and categories of matrices, in Russian, Investi-
gations on the theory of representations, Zap. Naucn. Sem. Leningrad. Otdel.
Mat. Inst. Steklov. (LOMI), 28 (1972), 144-153.
- S. Ebrahimi Atani, On pure-injective modules over pullback rings, Comm. Al-
gebra, 28(9) (2000), 4037-4069.
- S. Ebrahimi Atani, On secondary modules over Dedekind domains, Southeast
Asian Bull. Math, 25(1) (2001), 1-6.
- S. Ebrahimi Atani, On secondary modules over pullback rings, Comm. Algebra,
30(6) (2002), 2675-2685.
- S. Ebrahimi Atani, Indecomposable weak multiplication modules over Dedekind
domains, Demonstratio Math., 41(1) (2008), 33-43.
- R. Ebrahimi Atani and S. Ebrahimi Atani, Comultiplication modules over a
pullback of Dedekind domains, Czechoslovak Math. J., 59 (2009), 1103-1114.
- R. Ebrahimi Atani and S. Ebrahimi Atani, Weak comultiplication modules over
a pullback of commutative local Dedekind domains, Algebra Discrete Math., 1
(2009), 1-13.
- S. Ebrahimi Atani and F. Farzalipour, Weak multiplication modules over a
pullback of Dedekind domains, Colloq. Math., 114(1) (2009), 99-112.
- S. Ebrahimi Atani and M. Sedghi Shanbeh Bazari, Absorbing multiplication
modules over pullback rings, Int. Electron. J. Algebra, 21 (2017), 76-90.
- A. Facchini, Fiber products and Morita duality for commutative rings, Rend.
Sem. Mat. Univ. Padova, 67 (1982), 143-159.
- A. Facchini and P. Vamos, Injective modules over pullbacks, J. London Math.
Soc., 31 (1985), 425-438.
- J. Haefner and L. Klingler, Special quasi-triads and integral group rings of
nite representation type I, J. Algebra, 158(2) (1993), 279-322.
- J. Haefner and L. Klingler, Special quasi-triads and integral group rings of
nite representation type II, J. Algebra, 158(2) (1993), 323-374.
- I. Kaplansky, Modules over Dedekind rings and valuation rings, Trans. Amer.
Math., Soc., 72 (1952), 327-340.
- L. Klingler, Integral representations of groups of square-free order, J. Algebra,
129(1) (1990), 26-74.
- L. S. Levy, Modules over pullbacks and subdirect sums, J. Algebra, 71(1) (1981),
50-61.
- L. S. Levy, Mixed modules over ZG, G cyclic of prime order, and over related
Dedekind pullbacks, J. Algebra, 71(1) (1981), 62-114.
- L. S. Levy, Modules over Dedekind-like rings, J. Algebra, 93(1) (1985), 1-116.
- R. L. McCasland, M. E. Moore and P. F. Smith, On the spectrum of a module
over a commutative ring, Comm. Algebra, 25(1) (1997), 79-103.
- M. E. Moore and S. J. Smith, Prime and radical submodules of modules over
commutative rings, Comm. Algebra, 30(10) (2002), 5037-5064.
- L. A. Nazarova and A. V. Roiter, Finitely generated modules over a dyad of
two local Dedekind rings, and nite groups which possess an abelian normal
divisor of index p, Izv. Akad. Nauk SSSR Ser. Mat., 33 (1969), 65-89.
- Sh. Payrovi and S. Babaei, On the 2-absorbing submodules, Iran. J. Math. Sci.
Inform., 10(1) (2015), 131-137.
- M. Prest, Model Theory and Modules, London Mathematical Society Lecture
Note Series, 130, Cambridge University Press, Cambridge, 1988.
- M. Prest, Ziegler spectra of tame hereditary algebras, J. Algebra, 207(1) (1998),
146-164.
- C. M. Ringel, Some algebraically compact modules I, Abelian groups and mod-
ules (Padova, 1994), Math. Appl., 343, Kluwer Acad. Publ., Dordrecht, (1995),
419-439.
- C. M. Ringel, The Ziegler spectrum of a tame hereditary algebra, Colloq. Math.,
76(1) (1998), 105-115.
- D. Simson, Linear Representations of Partially Ordered Sets and Vector Space
Categories, Algebra, Logic and Applications, Vol. 4, Gordon and Breach Sci-
ence Publishers, Montreux, 1992.
- D. Simson, On Corner type endo-wild algebras, J. Pure Appl. Algebra, 202(1-3)
(2005), 118-132.
- R. B. War eld, Jr., Purity and algebraic compactness for modules, Paci c J.
Math., 28 (1969), 699-719.
- A. N. Wiseman, Projective modules over pullback rings, Math. Proc. Cam-
bridge Philos. Soc., 97(3) (1985), 399-406.
- A. Youse an Darani and F. Soheilnia, 2-Absorbing and weakly 2-absorbing
submodules, Thai J. Math., 9(3) (2011), 577-584.
- M. Ziegler, Model theory of modules, Ann. Pure Appl. Logic, 26(2) (1984),
149-213.